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Orthogonalized spatial multiplexing (OSM) systems with optimal precoding, denoted by POSM, was recently proposed which allows a single-symbol decodable maximum likelihood receiver in closed-loop multiple-input multiple-output (MIMO) systems. It was shown that the performance of the POSM is identical to that of the optimal closed-loop MIMO system in terms of the minimum distance. In this letter, we derive an exact symbol error rate (SER) expression of the POSM for 4-QAM and 16-QAM in Rayleigh fading channels. By using polar coordinates and the singular value distributions, the final expression of the SER can be evaluated with a single-integral form. Also, in the high SNR regime, we obtain a simple average SER expression of the POSM which shows that the POSM with two transmitting antennas achieves full diversity. Simulation results confirm the accuracy of our derived analysis.